Cognition and Student Learning Education Research

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Carnegie Mellon University Project Abstract
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Current information about this program can be found under the Education Research program.

Principal Investigator: Robert Siegler
Title: Improving Children’s Pure Numerical Estimation

Purpose: The ability to estimate numerical magnitude is important, not only because of its role in mathematical thinking but also because it is a part of children’s lives in and out of school. Estimation is also related to other aspects of mathematical ability, including arithmetic skill, conceptual understanding of computational procedures, and math achievement test scores. Although research on estimation is limited, we do know that children’s skill at estimation is poor. Prior research conducted by this research team has demonstrated that a major reason for children’s poor skill is that they rely on logarithmic rather than linear representations of numerical magnitudes. In other words, children’s abilities to discriminate between the magnitudes of numbers decreases sharply as these magnitudes increase. Preliminary evidence suggests that increasing young children’s use of appropriate representations of numerical magnitudes would improve their estimation and, by extension, their math achievement. The researchers have developed two interventions—one for preschool children and one for young elementary school children to support the acquisition of linear representations of numerical magnitudes. The purpose of this research project is to test whether learning produced by these interventions lasts over time, generalizes to other estimation tasks, enhances arithmetic learning, and can be scaled up to the classroom level. At the conclusion of this project, the research team will have validated both instructional interventions for use in one-on-one settings and in whole group instruction.

Setting: Participating children attend Head Start and childcare centers and public and Catholic elementary schools in the Pittsburgh area.

Population: The participants are 440 children. These include 240 4-year-olds from low-income, predominately African American, Head Start, and childcare centers and 200 white and African American second- and third-graders from low- and middle-income backgrounds.

Intervention: A board game The Great Race is used to teach children linear representations of numerical magnitude for numbers between 0-10. A second technique, The 150 Procedure, asks students to generate estimations at an optimal point on the number line and provides feedback to students. The 150 Procedure is used to help children improve their estimation skills on number lines from 0-1,000.

Research Design and Methods: At least seven different experiments are being carried out to test the effect of this instructional intervention on estimation skill. In the experiments with the second-graders, the researchers are examining instructional techniques for improving children’s estimation skills within a 1-1,000 range. The researchers also are examining the influence of The 150 Procedure when implemented at the classroom level. In the school-based studies, classrooms are randomly assigned to condition.

Control Condition: The game board used in the control conditions for the evaluation of the effect of The Great Race is identical to The Great Race game board except that it does not include the numbers 1 to 10 ordered from left to right printed on the 10 squares on the game board. Children use the color of the squares to play the game in the control condition. In the experimental evaluation of The 150 Procedure, experimental and control children receive the same problems but control children do not receive feedback on the accuracy of their answers.

Key Measures: Almost all of the materials are pencil and paper or computerized estimation and arithmetic problems. In the elementary school studies, math achievement scores are being obtained.

Data Analytic Strategy: Analysis of variance and t-test techniques are used to compare student outcomes across experimental conditions.

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Last Modified: 11/30/2006